simplify ln(2/9)

Solution

simplify

ln (\frac{2}{9})

ln (2) - 2 ln (3)

Decimal Notation

- 1.50407 \dots

Solution steps

ln (\frac{2}{9})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{2}{9}) = ln (2) - ln (9)

= ln (2) - ln (9)

ln (9) = 2 ln (3)

= ln (2) - 2 ln (3)

lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{4}})

lo g_{10} (x y^{2})

2 lo g_{2} (x) + 3 lo g_{2} (y)

ln (x^{2} - 1) - ln (x + 1)

\frac{7}{4} ln (x) - \frac{5}{4} ln (y) - \frac{1}{4} ln (z) + \frac{1}{4} ln (x)